Not able to link quick access pin of old customer Id with the new customer Id

As long as I can remember using the option on my device before ( now I am no longer a HDFC bank customer), when you request new pin there should be a pop up that would ask you to deregister from the old device. If you are getting this option, you can use it to deregister the old device.
However, I would consider it the best option to get in touch with the customer care service. They should be able to solve your problem easily. Most of the time, such actions are handled with administrative privileges and only way to get it done would be to contact the customer care service.
The exact situation in your case is not understood properly. You should have received a new access PIN with your customer ID.
If you have access to your netbanking account, login to the same and find if there is any option for deregistering the earlier customer ID or device. If you can do that, it should be quite easy to set new access PIN.
In any case, it may be a good idea to contact your local branch. If you fail to get a proper response, get in touch with the customer care with complete details.

As per the normal bank rules, the Bank is always supposed to provide with a quick access pin for each customer whenever they issue a new customer ID. You didn't mention in your question, how did you receive this new customer ID, whether through the bank directly, through a printed mail sent by the bank, or through electronic media like email or phone.
But whichever is the case, it is evident that the bank will surely provide you with a quick access number for you new customer ID, which you can change afterwards. In no way, you can use the earlier pin number for the new user ID.
So, for this, you need to either contact your branch, or you can send an email enquiry to the internet banking customer care support. They will provide you with either an OTP to log in, or they can provide with a temporary password which you can change later.
Another thing is, if you have tried with a wrong password combination more than three times a day, your online banking will be blocked. In that case, you have to follow the same steps discussed above to get it unblocked. So I think that is the only way, this issue can be resolved.

The current premise of not recognizing the new customer ID and quick access PIN is probably because your Mobile app has stored the quick access pin of old ID in database. So as long as your current app is registered with this mobile number and has these settings stored, then this issue might arise.

You can register this by uninstalling the app. Reset the phone settings and change your customer ID phone number if you have dual SIM. And during SMS verification of the app process you can pinpoint to your other SIM for verification. This is the method every bank suggests for verifying your new customer ID on the phone or tablet.

Do note that this is not a bug or any feature issue, but your phone number and App ID gets locked to one device. This sort of locking makes it impossible for you to use it with another customer ID. You can either use alternative phone number or use dual SIM mode and get rid of app and reinstall with new SIM during activation. That way the customer ID you wish to use gets locked for that number and device ID.